Airfoil for a first stage nozzle guide vane

ABSTRACT

The present invention provides an airfoil for a first stage nozzle guide vane having an external surface with first and second sides. The external surface extends spanwise between a hub and a tip and streamwise between a leading edge and a trailing edge of the airfoil. The external surface includes a contour substantially defined by Table 1 as listed in the specification.

RELATED APPLICATIONS

The present application claims the benefit of U.S. patent application Ser. No. 60/755,498 filed Dec. 29, 2005, which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to improved airfoil geometry, and more particularly to a high efficiency airfoil for a turbine nozzle guide vane in a gas turbine engine.

BACKGROUND

Gas turbine engine designers continuously work to improve engine efficiency, to reduce operating costs of the engine, and to reduce specific exhaust gas emissions such as NOx, CO2, CO, unburnt hydrocarbons, and particulate matter. The specific fuel consumption (SFC) of an engine is inversely proportional to the overall thermal efficiency of the engine, thus, as the SFC decreases the fuel efficiency of the engine increases. Furthermore, specific exhaust gas emissions typically decrease as the engine becomes more efficient. The thermal efficiency of the engine is a function of component efficiencies, cycle pressure ratio and turbine inlet temperature. The present invention contemplates increased thermal efficiency for a gas turbine engine by improving turbine efficiency through a new aerodynamic design of an airfoil for a first stage nozzle guide vane.

SUMMARY

The present invention provides an airfoil with an external surface having first and second sides, the external surface extends spanwise between a hub and a tip and streamwise between a leading edge and a trailing edge. The external surface has a contour substantially defined by Table 1 as listed in the specification.

In another aspect of the present invention, a turbine nozzle guide vane assembly for a gas turbine engine can include an inner shroud having an upper surface and a lower surface, the upper surface of the inner shroud partially defining an inner flow path wall. An airfoil can extend radially outward from the upper surface of the inner shroud relative to an axis of rotation of the gas turbine engine. The airfoil includes first and second three-dimensional external surfaces that extend between a hub and a tip in a spanwise direction and between a leading edge and a trailing edge in a streamwise direction. A Cartesian coordinate array having X,Y and Z axis coordinates listed in Table 1 of the specification defines the first and second external surfaces of the airfoil.

Another aspect of the present invention provides for a method of forming an airfoil for a turbine nozzle guide vane. The method includes forming a contoured three-dimensional external surface of an airfoil defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured in a radial direction from a longitudinal axis, the X axis coordinates are generally measured normal to the Z axis in a streamwise direction, and the Y axis coordinates are generally measured normal to the Z axis and normal to the X axis.

Another aspect of the present invention provides for a method of forming an airfoil for a turbine nozzle guide vane. The method includes forming a contoured three-dimensional external surface of an airfoil defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured from an engine centerline axis, the X axis coordinates are generally measured normal to the Z axis in a streamwise direction, and the Y axis coordinates are generally measured normal to the Z axis and normal to the X axis.

BRIEF DESCRIPTION OF THE DRAWINGS

The description herein makes reference to the accompanying drawings wherein like reference numerals refer to like parts throughout the several views, and wherein:

FIG. 1 is a schematic representation of a gas turbine engine;

FIG. 2 is a cross-sectional view of a turbine module for the gas turbine engine of FIG. 1;

FIG. 3 is a perspective view of a first stage turbine nozzle guide vane segment illustrated in FIG. 2;

FIG. 4 is a front view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;

FIG. 5 is a back view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;

FIG. 6 is a right view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;

FIG. 7 is a left view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3;

FIG. 8 is a top view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3; and

FIG. 9 is a bottom view of the first stage turbine nozzle guide vane segment illustrated in FIG. 3.

DETAILED DESCRIPTION

For purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiments illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated device, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates.

Referring to FIG. 1, a schematic view of a gas turbine engine 10 is depicted. While the gas turbine engine 10 is illustrated with one spool (i.e. one shaft connecting a turbine and a compressor), it should be understood that the present invention is not limited to any particular engine design or configuration and as such may be used in multi spool engines of the aero or power generation type. The gas turbine engine 10 will be described generally, however significant details regarding general gas turbine engines will not be presented herein as it is believed that the theory of operation and general parameters of gas turbine engines are well known to those of ordinary skill in the art.

The gas turbine engine 10 includes an inlet section 12, a compressor section 14, a combustor section 16, a turbine section 18, and an exhaust section 20. In operation, air is drawn in through the inlet 12 and compressed to a high pressure relative to ambient pressure in the compressor section 14. The air is mixed with fuel in the combustor section 16 wherein the fuel/air mixture burns and produces a high temperature and pressure working fluid from which the turbine section 18 extracts power. The turbine section 18 is mechanically coupled to the compressor section 14 via a shaft 22. The shaft 22 rotates about a centerline axis 24 that extends axially along the longitudinal axis of the engine 10, such that as the turbine section 18 rotates due to the forces generated by the high pressure working fluid, the compressor section 14 is rotatingly driven by the turbine section 18 to produce compressed air. A portion of the power extracted from the turbine section 18 can be utilized to drive a secondary device 26, which in one embodiment can be an electrical generator. The electrical generator can be run at a substantially constant speed that is appropriate for a desired power grid frequency; a non-limiting example being 50 or 60 Hz. Alternatively the secondary device 26 can be in the form of a compressor or pump for use in fluid pipelines such as oil or natural gas lines.

Referring now to FIG. 2, a partial cross section of the turbine section 18 is shown therein. As the working fluid exits the combustor section 16, the working fluid is constrained between an inner flow path wall 31 and an outer flow path wall 33 as it flows through the turbine section 18. The turbine section 18 includes a turbine inlet or first stage nozzle guide vane (NGV) assembly 30. The first stage NGV assembly 30 includes a plurality of static vanes or airfoils 32 positioned circumferentially around a flow path annulus of the engine 10. The first stage NGV assembly 30 is operable for accelerating and turning the flow of working fluid to a desired direction, as the working fluid exits the combustor section 16 and enters the turbine section 18.

Each airfoil 32 of the first stage NGV assembly 30 extends between a leading edge 34 and a trailing edge 36 in the stream wise direction and between an inner shroud 38 and an outer shroud 40 in the spanwise direction. It should be understood that the terms leading edge and trailing edge are defined relative to the general flow path of the working fluid, such that the working fluid first passes the leading edge and subsequently passes the trailing edge of a particular airfoil. The inner and outer shrouds 38, 40 form a portion of the inner and outer flow path walls 31, 33 respectively at that location in the engine 10. The first stage NGV assembly 30 will be the described in more detail below.

The turbine section 18 further includes a first stage turbine assembly 42 positioned downstream of the first stage NGV assembly 30. The first stage turbine assembly 42 includes a first turbine wheel 44 which is comprised of a first turbine disk 46 having a plurality of first stage turbine blades 48 coupled thereto. It should be noted here that in one preferred embodiment the turbine blades 48 and the disk 46 can be separate components, but that the present invention contemplates other forms such as a turbine wheel having the blades and disk integrally formed together. This type of component is commonly called a “BLISK,” short for a “Bladed Disk,” by those working in the gas turbine engine industry.

Each turbine blade 48 includes an airfoil 50 that rotates with the turbine disk 46. Each airfoil 50 extends between a leading edge 52 and a trailing edge 54 in the stream wise direction and between an inner shroud or platform 56 and an outer shroud 58 in the spanwise direction. The disk 46 may include one or more seals 60 extending forward or aft in the streamwise direction. The seals 60, sometimes called rotating knife seals, limit the leakage of working fluid from the desired flowpath. The first stage turbine assembly 42 is operable for extracting energy from the working fluid via the airfoils 50 which in turn cause the turbine wheel 44 to rotate and drive the shaft 22.

Directly downstream of the first stage turbine assembly 42 is a second stage nozzle guide vane (NGV) assembly 70. The second stage NGV assembly 70 includes a plurality of static vanes or airfoils 72 positioned circumferentially around the flow path of the engine 10. The airfoils 72 of the second stage NGV assembly 70 are operable for accelerating and turning the working fluid flow to a desired direction as the working fluid exits the second stage NGV assembly 70. Each airfoil 72 extends between a leading edge 74 and a trailing edge 76 in the stream wise direction and between an inner shroud 78 and an outer shroud 80 in the spanwise direction. The inner and outer shrouds 78, 80 form a portion of the inner and outer flow path walls 31, 33 respectively at that location in the engine 10.

A second stage turbine assembly 82 is positioned downstream of the second stage NGV assembly 70. The second stage turbine assembly 82 includes a second turbine wheel 84 which is comprised of a second turbine disk 86 having a plurality of second stage turbine blades 88 coupled thereto. Each turbine blade 88 includes an airfoil 90 that rotates with the turbine disk 86 when the engine 10 is running. Each airfoil 90 extends between a leading edge 92 and a trailing edge 94 in the stream wise direction and between an inner shroud or platform 96 and an outer shroud 98 in the spanwise direction. The disk 86 may include one or more seals 100 extending forward or aft in the streamwise direction. In this particular embodiment of the invention, the second stage turbine assembly 82 is connected to the first stage turbine assembly 42 and therefore increases the power delivered to the shaft 22.

A third stage nozzle guide vane (NGV) assembly 110 is located downstream of the second stage turbine assembly 82. The third stage NGV assembly 110 includes a plurality of static vanes or airfoils 112 positioned circumferentially around the flowpath of the engine 10. The airfoils 112 of the third stage NGV assembly 110 are operable for accelerating and turning the working fluid flow to a desired direction as the working fluid exits the third stage NGV assembly 110. Each airfoil 112 extends between a leading edge 114 and a trailing edge 116 in the streamwise direction and between an inner shroud 118 and an outer shroud 120 in the spanwise direction. The inner and outer shrouds 118, 120 form a portion of the inner and outer flow path walls 31, 33 respectively at that location in the engine 10.

A third stage turbine assembly 130 is positioned downstream of the third stage NGV 110. The third stage turbine assembly 130 includes a third turbine wheel 132 which is comprised of a third turbine disk 134 having a plurality of third stage turbine blades 136 coupled thereto. Each turbine blade 136 includes an airfoil 138 that rotates with the turbine disk 134 when the engine 10 is running. Each airfoil 138 extends between a leading edge 140 and a trailing edge 142 in the stream wise direction and between an inner shroud or platform 144 and an outer shroud 146 in the spanwise direction. The third disk 134 may also include one or more seals 148 extending forward or aft of the disk 134 in the streamwise direction. Similar to the second stage turbine assembly 82, the third stage turbine assembly 130 is also connected to the first stage turbine assembly 42 and therefore further increases the power delivered to the shaft 22.

Although not shown in each of the drawings it should be understood that the airfoils for both the turbine blades and turbine nozzle guide vanes may include internal cooling flow passages and apertures extending through portions of the external surfaces of the airfoil. Pressurized cooling fluid can then flow from the internal passages through the apertures to cool the external surface of the airfoils as would be known to those skilled in the art. In this manner, the engine 10 may be run at the higher turbine inlet temperatures, and thus produce higher thermal efficiencies while still providing adequate component life as measured by such parameters as high cycle fatigue limits, low cycle fatigue limits, and creep, etc.

It should be further noted that the airfoils may include coatings to increase component life. The coatings can be of the thermal barrier type and/or the radiation barrier type. Thermal barrier coatings have relatively low heat transfer coefficients which help to reduce the heat load that the cooling fluid is required to dissipate. Thermal barrier coatings are typically ceramic based and can include mullite and zirconia based composites, although other types of coatings are contemplated herein. Radiation barrier coatings operate to reduce radiation heat transfer to the coated component by having highly reflective external surfaces such that radiation emanating from the high temperature exhaust gas is at least partially reflected away and not absorbed by the component. Radiation barrier coatings can include materials from high temperature chromium based alloys as is known to those skilled in the art. The radiation barrier coatings and thermal barrier coatings can be used to coat the entire airfoil, but alternate embodiments include a partial coating and/or a coating with intermittent discontinuities formed therein.

Referring now to FIGS. 3 through 9, the first stage nozzle guide vane assembly 30 will be described in more detail. As described previously, the nozzle guide vane assembly 30 includes an inner shroud 38 wherein an outer surface 150 of the shroud defines a portion of the inner flow path wall 31 at that particular location in the engine 10. A plurality of airfoils 32 extends radially outward from the outer surface 150 of the shroud 38 from a hub 152 toward a tip 154. Each airfoil 32 is attached to the shroud 38 proximate the hub 152 of the airfoil 32. The airfoils 32 can be integrally formed with the shroud 38 through a casting process or the like or alternatively may be mechanically joined via welding, brazing or by any other joining method known to those skilled in the art. An outer shroud 40 can be attached to the airfoil 32 proximate the tip 154 of the airfoil 32. The outer shroud 40 includes an inner surface 156 which forms a portion of the outer flow path 33 in the turbine section 18.

The first stage nozzle guide vane assembly 30 further includes an outer lug 160 positioned above each airfoil. The lugs 160 are operable for reacting torque loads produced by the airfoils through the frame (not shown) of the aircraft engine 10. A plurality of coolant inlets 162 can be formed in the outer shroud 40 to provide cooling fluid to each airfoil 32. The cooling fluid extracts heat load from each airfoil 32 and is ejected through coolant outlet holes 164 into the flow path of the working fluid.

Each airfoil 32 includes an external surface 161 having first and second sides 163, 165 sometimes called pressure and suction sides respectively. The external surface 161 of the airfoil 32 provides aerodynamic control of the flow of working fluid so as to optimize efficiency in the turbine section 18. The external surface 161 of the airfoil 32 is substantially defined by Table 1 listed below. Table 1 lists data points in Cartesian coordinates that define the external surface of the airfoil 32 at discrete locations. The Z axis coordinates are generally measured radially outward from a reference location. In one form the reference location is the engine centerline axis and in another form the reference location is the inner shroud 38 from the hub 152. The Z axis defines an imaginary stacking axis from which the contoured external surface is formed. The term “stacking axis,” as it is typically used by aerodynamic design engineers, is nominally defined normal to the inner shroud 38 or in a radial direction from the axis of rotation, but in practice can “lean” or “tilt” in a desired direction to satisfy mechanical design criteria as is known to those skilled in the art. The lean or tilt angle is typically within 10°-25° of the normal plane in any direction relative to the inner shroud 38, but can vary with larger angles as necessary to satisfy mechanical design criteria. The X axis coordinates are generally measured normal to the stacking axis in a streamwise direction. The Y axis coordinates are generally measured normal to the stacking axis and normal to the X axis. The airfoil 32 defined by Table 1 improves the first stage turbine nozzle guide vane efficiency by 0.94% over prior art designs.

While the external surface of airfoil 32 is defined by discrete points, the surface can be “smoothed” between these discrete points by parametric spline fit techniques and the like. One such method called numerical uniform rational B-spline (NURB-S) is employed by software run on Unigraphics® computer aided design workstations. The data splines can be formed in the streamwise direction and/or the spanwise direction of the airfoil 32. Other surface smoothing techniques known to those skilled in the art are also contemplated by the present invention.

The airfoils of the present invention can be formed from any manufacturing process known to those skilled in the art. One such process is an investment casting method whereby the entire first stage NGV assembly 30 is integrally cast as a one-piece component. Alternatively the first stage NGV assembly 30 can be formed in multiple pieces and bonded together. In another form, the first stage NGV assembly 30 can be formed from wrought material and finished machined to a desired specification.

The present invention includes airfoils having an external surface formed within a manufacturing tolerance of ±0.025 inches with respect to any particular point in Table 1 or spline curve between discrete points. Furthermore, if the airfoil of the present invention has a material coating applied, the tolerance band can be increased to ±0.050 inches.

TABLE 1 Coordinates for airfoils on the first stage nozzle guide vane (in). A. Section height 11.75 X1 = −0.77808 Y1 = 0.42024 Z1 = 11.75000 X2 = −0.79849 Y2 = 0.44000 Z2 = 11.75000 X3 = −0.80884 Y3 = 0.46644 Z3 = 11.75000 X4 = −0.80727 Y4 = 0.49480 Z4 = 11.75000 X5 = −0.79406 Y5 = 0.51994 Z5 = 11.75000 X6 = −0.63813 Y6 = 0.61239 Z6 = 11.75000 X7 = −0.68171 Y7 = 0.59769 Z7 = 11.75000 X8 = −0.72325 Y8 = 0.57805 Z8 = 11.75000 X9 = −0.76086 Y9 = 0.55171 Z9 = 11.75000 X10 = −0.79406 Y10 = 0.51994 Z10 = 11.75000 X11 = 0.84940 Y11 = −0.90763 Z11 = 11.75000 X12 = 0.80838 Y12 = −0.79328 Z12 = 11.75000 X13 = 0.76302 Y13 = −0.68058 Z13 = 11.75000 X14 = 0.71490 Y14 = −0.56902 Z14 = 11.75000 X15 = 0.66489 Y15 = −0.45829 Z15 = 11.75000 X16 = 0.61286 Y16 = −0.34850 Z16 = 11.75000 X17 = 0.55811 Y17 = −0.24005 Z17 = 11.75000 X18 = 0.49988 Y18 = −0.13342 Z18 = 11.75000 X19 = 0.43746 Y19 = −0.02919 Z19 = 11.75000 X20 = 0.37011 Y20 = 0.07190 Z20 = 11.75000 X21 = 0.29690 Y21 = 0.16885 Z21 = 11.75000 X22 = 0.21777 Y22 = 0.26101 Z22 = 11.75000 X23 = 0.13239 Y23 = 0.34741 Z23 = 11.75000 X24 = 0.04001 Y24 = 0.42625 Z24 = 11.75000 X25 = −0.05947 Y25 = 0.49592 Z25 = 11.75000 X26 = −0.16587 Y26 = 0.55443 Z26 = 11.75000 X27 = −0.27882 Y27 = 0.59891 Z27 = 11.75000 X28 = −0.39720 Y28 = 0.62571 Z28 = 11.75000 X29 = −0.51837 Y29 = 0.63133 Z29 = 11.75000 X30 = −0.63813 Y30 = 0.61239 Z30 = 11.75000 X31 = 0.84940 Y31 = −0.90763 Z31 = 11.75000 X32 = 0.84911 Y32 = −0.91635 Z32 = 11.75000 X33 = 0.84299 Y33 = −0.92270 Z33 = 11.75000 X34 = 0.83430 Y34 = −0.92329 Z34 = 11.75000 X35 = 0.82752 Y35 = −0.91773 Z35 = 11.75000 X36 = −0.65696 Y36 = 0.38301 Z36 = 11.75000 X37 = −0.55257 Y37 = 0.35743 Z37 = 11.75000 X38 = −0.44921 Y38 = 0.32798 Z38 = 11.75000 X39 = −0.34757 Y39 = 0.29305 Z39 = 11.75000 X40 = −0.24847 Y40 = 0.25149 Z40 = 11.75000 X41 = −0.15293 Y41 = 0.20232 Z41 = 11.75000 X42 = −0.06214 Y42 = 0.14485 Z42 = 11.75000 X43 = 0.02370 Y43 = 0.08019 Z43 = 11.75000 X44 = 0.10618 Y44 = 0.01128 Z44 = 11.75000 X45 = 0.18564 Y45 = −0.06109 Z45 = 11.75000 X46 = 0.26184 Y46 = −0.13688 Z46 = 11.75000 X47 = 0.33542 Y47 = −0.21524 Z47 = 11.75000 X48 = 0.40658 Y48 = −0.29579 Z48 = 11.75000 X49 = 0.47506 Y49 = −0.37862 Z49 = 11.75000 X50 = 0.54079 Y50 = −0.46366 Z50 = 11.75000 X51 = 0.60352 Y51 = −0.55094 Z51 = 11.75000 X52 = 0.66313 Y52 = −0.64038 Z52 = 11.75000 X53 = 0.71980 Y53 = −0.73170 Z53 = 11.75000 X54 = 0.77420 Y54 = −0.82440 Z54 = 11.75000 X55 = 0.82752 Y55 = −0.91773 Z55 = 11.75000 X56 = −0.77808 Y56 = 0.42024 Z56 = 11.75000 X57 = −0.74932 Y57 = 0.40679 Z57 = 11.75000 X58 = −0.71885 Y58 = 0.39772 Z58 = 11.75000 X59 = −0.68793 Y59 = 0.39026 Z59 = 11.75000 X60 = −0.65696 Y60 = 0.38301 Z60 = 11.75000 B. Section height 12.25 X1 = −0.79201 Y1 = 0.46381 Z1 = 12.25000 X2 = −0.80457 Y2 = 0.43888 Z2 = 12.25000 X3 = −0.80588 Y3 = 0.41100 Z3 = 12.25000 X4 = −0.79570 Y4 = 0.38502 Z4 = 12.25000 X5 = −0.77576 Y5 = 0.36549 Z5 = 12.25000 X6 = −0.64788 Y6 = 0.55619 Z6 = 12.25000 X7 = −0.68803 Y7 = 0.53993 Z7 = 12.25000 X8 = −0.72638 Y8 = 0.51983 Z8 = 12.25000 X9 = −0.76141 Y9 = 0.49441 Z9 = 12.25000 X10 = −0.79201 Y10 = 0.46381 Z10 = 12.25000 X11 = 0.84952 Y11 = −0.94682 Z11 = 12.25000 X12 = 0.80824 Y12 = −0.83178 Z12 = 12.25000 X13 = 0.76305 Y13 = −0.71821 Z13 = 12.25000 X14 = 0.71507 Y14 = −0.60580 Z14 = 12.25000 X15 = 0.66478 Y15 = −0.49439 Z15 = 12.25000 X16 = 0.61203 Y16 = −0.38413 Z16 = 12.25000 X17 = 0.55638 Y17 = −0.27531 Z17 = 12.25000 X18 = 0.49730 Y18 = −0.16831 Z18 = 12.25000 X19 = 0.43428 Y19 = −0.06359 Z19 = 12.25000 X20 = 0.36660 Y20 = 0.03819 Z20 = 12.25000 X21 = 0.29350 Y21 = 0.13612 Z21 = 12.25000 X22 = 0.21444 Y22 = 0.22932 Z22 = 12.25000 X23 = 0.12897 Y23 = 0.31666 Z23 = 12.25000 X24 = 0.03631 Y24 = 0.39631 Z24 = 12.25000 X25 = −0.06395 Y25 = 0.46611 Z25 = 12.25000 X26 = −0.17186 Y26 = 0.52334 Z26 = 12.25000 X27 = −0.28681 Y27 = 0.56452 Z27 = 12.25000 X28 = −0.40702 Y28 = 0.58576 Z28 = 12.25000 X29 = −0.52901 Y29 = 0.58360 Z29 = 12.25000 X30 = −0.64788 Y30 = 0.55619 Z30 = 12.25000 X31 = 0.84952 Y31 = −0.94682 Z31 = 12.25000 X32 = 0.84925 Y32 = −0.95559 Z32 = 12.25000 X33 = 0.84306 Y33 = −0.96194 Z33 = 12.25000 X34 = 0.83430 Y34 = −0.96255 Z34 = 12.25000 X35 = 0.82743 Y35 = −0.95703 Z35 = 12.25000 X36 = −0.62568 Y36 = 0.31791 Z36 = 12.25000 X37 = −0.52382 Y37 = 0.29214 Z37 = 12.25000 X38 = −0.42300 Y38 = 0.26258 Z38 = 12.25000 X39 = −0.32421 Y39 = 0.22685 Z39 = 12.25000 X40 = −0.22808 Y40 = 0.18447 Z40 = 12.25000 X41 = −0.13539 Y41 = 0.13507 Z41 = 12.25000 X42 = −0.04712 Y42 = 0.07812 Z42 = 12.25000 X43 = 0.03686 Y43 = 0.01500 Z43 = 12.25000 X44 = 0.11765 Y44 = −0.05217 Z44 = 12.25000 X45 = 0.19547 Y45 = −0.12276 Z45 = 12.25000 X46 = 0.27033 Y46 = −0.19648 Z46 = 12.25000 X47 = 0.34261 Y47 = −0.27273 Z47 = 12.25000 X48 = 0.41237 Y48 = −0.35130 Z48 = 12.25000 X49 = 0.47946 Y49 = −0.43216 Z49 = 12.25000 X50 = 0.54382 Y50 = −0.51521 Z50 = 12.25000 X51 = 0.60541 Y51 = −0.60033 Z51 = 12.25000 X52 = 0.66420 Y52 = −0.68741 Z52 = 12.25000 X53 = 0.72037 Y53 = −0.77621 Z53 = 12.25000 X54 = 0.77441 Y54 = −0.86631 Z54 = 12.25000 X55 = 0.82743 Y55 = −0.95703 Z55 = 12.25000 X56 = −0.77576 Y56 = 0.36549 Z56 = 12.25000 X57 = −0.73999 Y57 = 0.34895 Z57 = 12.25000 X58 = −0.70222 Y58 = 0.33742 Z58 = 12.25000 X59 = −0.66401 Y59 = 0.32742 Z59 = 12.25000 X60 = −0.62568 Y60 = 0.31791 Z60 = 12.25000 C. Section height 12.75 X1 = −0.79009 Y1 = 0.40814 Z1 = 12.75000 X2 = −0.80217 Y2 = 0.38334 Z2 = 12.75000 X3 = −0.80322 Y3 = 0.35578 Z3 = 12.75000 X4 = −0.79305 Y4 = 0.33014 Z4 = 12.75000 X5 = −0.77337 Y5 = 0.31081 Z5 = 12.75000 X6 = −0.79009 Y6 = 0.40814 Z6 = 12.75000 X7 = −0.75933 Y7 = 0.43976 Z7 = 12.75000 X8 = −0.72335 Y8 = 0.46536 Z8 = 12.75000 X9 = −0.68446 Y9 = 0.48630 Z9 = 12.75000 X10 = −0.64382 Y10 = 0.50364 Z10 = 12.75000 X11 = −0.64382 Y11 = 0.50364 Z11 = 12.75000 X12 = −0.52602 Y12 = 0.53407 Z12 = 12.75000 X13 = −0.40446 Y13 = 0.53943 Z13 = 12.75000 X14 = −0.28422 Y14 = 0.52053 Z14 = 12.75000 X15 = −0.16914 Y15 = 0.48078 Z15 = 12.75000 X16 = −0.06135 Y16 = 0.42407 Z16 = 12.75000 X17 = 0.03844 Y17 = 0.35418 Z17 = 12.75000 X18 = 0.13040 Y18 = 0.27424 Z18 = 12.75000 X19 = 0.21518 Y19 = 0.18670 Z19 = 12.75000 X20 = 0.29350 Y20 = 0.09332 Z20 = 12.75000 X21 = 0.36595 Y21 = −0.00469 Z21 = 12.75000 X22 = 0.43333 Y22 = −0.10626 Z22 = 12.75000 X23 = 0.49639 Y23 = −0.21056 Z23 = 12.75000 X24 = 0.55574 Y24 = −0.31702 Z24 = 12.75000 X25 = 0.61181 Y25 = −0.42525 Z25 = 12.75000 X26 = 0.66487 Y26 = −0.53499 Z26 = 12.75000 X27 = 0.71523 Y27 = −0.64599 Z27 = 12.75000 X28 = 0.76304 Y28 = −0.75812 Z28 = 12.75000 X29 = 0.80805 Y29 = −0.87139 Z29 = 12.75000 X30 = 0.84963 Y30 = −0.98597 Z30 = 12.75000 X31 = 0.84963 Y31 = −0.98597 Z31 = 12.75000 X32 = 0.84941 Y32 = −0.99477 Z32 = 12.75000 X33 = 0.84322 Y33 = −1.00116 Z33 = 12.75000 X34 = 0.83443 Y34 = −1.00183 Z34 = 12.75000 X35 = 0.82748 Y35 = −0.99636 Z35 = 12.75000 X36 = 0.82748 Y36 = −0.99636 Z36 = 12.75000 X37 = 0.77282 Y37 = −0.90525 Z37 = 12.75000 X38 = 0.71707 Y38 = −0.81480 Z38 = 12.75000 X39 = 0.65922 Y39 = −0.72569 Z39 = 12.75000 X40 = 0.59883 Y40 = −0.63827 Z40 = 12.75000 X41 = 0.53572 Y41 = −0.55280 Z41 = 12.75000 X42 = 0.46986 Y42 = −0.46944 Z42 = 12.75000 X43 = 0.40119 Y43 = −0.38837 Z43 = 12.75000 X44 = 0.32970 Y44 = −0.30977 Z44 = 12.75000 X45 = 0.25550 Y45 = −0.23373 Z45 = 12.75000 X46 = 0.17851 Y46 = −0.16052 Z46 = 12.75000 X47 = 0.09856 Y47 = −0.09056 Z47 = 12.75000 X48 = 0.01553 Y48 = −0.02428 Z48 = 12.75000 X49 = −0.07100 Y49 = 0.03735 Z49 = 12.75000 X50 = −0.16181 Y50 = 0.09245 Z50 = 12.75000 X51 = −0.25659 Y51 = 0.14041 Z51 = 12.75000 X52 = −0.35445 Y52 = 0.18174 Z52 = 12.75000 X53 = −0.45496 Y53 = 0.21611 Z53 = 12.75000 X54 = −0.55740 Y54 = 0.24428 Z54 = 12.75000 X55 = −0.66038 Y55 = 0.27043 Z55 = 12.75000 X56 = −0.66038 Y56 = 0.27043 Z56 = 12.75000 X57 = −0.68944 Y57 = 0.27831 Z57 = 12.75000 X58 = −0.71830 Y58 = 0.28688 Z58 = 12.75000 X59 = −0.74660 Y59 = 0.29712 Z59 = 12.75000 X60 = −0.77337 Y60 = 0.31081 Z60 = 12.75000 D. Section height 13.25 X1 = −0.78853 Y1 = 0.35300 Z1 = 13.25000 X2 = −0.80026 Y2 = 0.32825 Z2 = 13.25000 X3 = −0.80110 Y3 = 0.30088 Z3 = 13.25000 X4 = −0.79089 Y4 = 0.27546 Z4 = 13.25000 X5 = −0.77133 Y5 = 0.25629 Z5 = 13.25000 X6 = −0.78853 Y6 = 0.35300 Z6 = 13.25000 X7 = −0.75795 Y7 = 0.38488 Z7 = 13.25000 X8 = −0.72193 Y8 = 0.41054 Z8 = 13.25000 X9 = −0.68302 Y9 = 0.43164 Z9 = 13.25000 X10 = −0.64247 Y10 = 0.44935 Z10 = 13.25000 X11 = −0.64247 Y11 = 0.44935 Z11 = 13.25000 X12 = −0.52558 Y12 = 0.48097 Z12 = 13.25000 X13 = −0.40467 Y13 = 0.48758 Z13 = 13.25000 X14 = −0.28484 Y14 = 0.46987 Z14 = 13.25000 X15 = −0.17002 Y15 = 0.43113 Z15 = 13.25000 X16 = −0.06252 Y16 = 0.37513 Z16 = 13.25000 X17 = 0.03696 Y17 = 0.30582 Z17 = 13.25000 X18 = 0.12864 Y18 = 0.22644 Z18 = 13.25000 X19 = 0.21316 Y19 = 0.13946 Z19 = 13.25000 X20 = 0.29120 Y20 = 0.04661 Z20 = 13.25000 X21 = 0.36340 Y21 = −0.05086 Z21 = 13.25000 X22 = 0.43072 Y22 = −0.15177 Z22 = 13.25000 X23 = 0.49395 Y23 = −0.25530 Z23 = 13.25000 X24 = 0.55363 Y24 = −0.36091 Z24 = 13.25000 X25 = 0.61010 Y25 = −0.46828 Z25 = 13.25000 X26 = 0.66356 Y26 = −0.57717 Z26 = 13.25000 X27 = 0.71421 Y27 = −0.68740 Z27 = 13.25000 X28 = 0.76223 Y28 = −0.79881 Z28 = 13.25000 X29 = 0.80748 Y29 = −0.91136 Z29 = 13.25000 X30 = 0.84974 Y30 = −1.02507 Z30 = 13.25000 X31 = 0.84974 Y31 = −1.02507 Z31 = 13.25000 X32 = 0.84960 Y32 = −1.03388 Z32 = 13.25000 X33 = 0.84347 Y33 = −1.04035 Z33 = 13.25000 X34 = 0.83468 Y34 = −1.04112 Z34 = 13.25000 X35 = 0.82765 Y35 = −1.03573 Z35 = 13.25000 X36 = 0.82765 Y36 = −1.03573 Z36 = 13.25000 X37 = 0.77319 Y37 = −0.94758 Z37 = 13.25000 X38 = 0.71771 Y38 = −0.86007 Z38 = 13.25000 X39 = 0.66040 Y39 = −0.77375 Z39 = 13.25000 X40 = 0.60082 Y40 = −0.68898 Z40 = 13.25000 X41 = 0.53877 Y41 = −0.60601 Z41 = 13.25000 X42 = 0.47414 Y42 = −0.52503 Z42 = 13.25000 X43 = 0.40684 Y43 = −0.44625 Z43 = 13.25000 X44 = 0.33684 Y44 = −0.36987 Z44 = 13.25000 X45 = 0.26415 Y45 = −0.29603 Z45 = 13.25000 X46 = 0.18877 Y46 = −0.22495 Z46 = 13.25000 X47 = 0.11063 Y47 = −0.15691 Z47 = 13.25000 X48 = 0.02962 Y48 = −0.09233 Z48 = 13.25000 X49 = −0.05456 Y49 = −0.03192 Z49 = 13.25000 X50 = −0.14240 Y50 = 0.02299 Z50 = 13.25000 X51 = −0.23384 Y51 = 0.07168 Z51 = 13.25000 X52 = −0.32822 Y52 = 0.11440 Z52 = 13.25000 X53 = −0.42524 Y53 = 0.15070 Z53 = 13.25000 X54 = −0.52456 Y54 = 0.18018 Z54 = 13.25000 X55 = −0.62484 Y55 = 0.20625 Z55 = 13.25000 X56 = −0.62484 Y56 = 0.20625 Z56 = 13.25000 X57 = −0.66241 Y57 = 0.21614 Z57 = 13.25000 X58 = −0.69984 Y58 = 0.22656 Z58 = 13.25000 X59 = −0.73667 Y59 = 0.23887 Z59 = 13.25000 X60 = −0.77133 Y60 = 0.25629 Z60 = 13.25000 E. Section height 13.75 X1 = −0.78730 Y1 = 0.29843 Z1 = 13.75000 X2 = −0.79882 Y2 = 0.27363 Z2 = 13.75000 X3 = −0.79947 Y3 = 0.24629 Z3 = 13.75000 X4 = −0.78913 Y4 = 0.22097 Z4 = 13.75000 X5 = −0.76951 Y5 = 0.20191 Z5 = 13.75000 X6 = −0.78730 Y6 = 0.29843 Z6 = 13.75000 X7 = −0.75545 Y7 = 0.33156 Z7 = 13.75000 X8 = −0.71767 Y8 = 0.35781 Z8 = 13.75000 X9 = −0.67688 Y9 = 0.37916 Z9 = 13.75000 X10 = −0.63435 Y10 = 0.39681 Z10 = 13.75000 X11 = −0.63435 Y11 = 0.39681 Z11 = 13.75000 X12 = −0.51812 Y12 = 0.42546 Z12 = 13.75000 X13 = −0.39846 Y13 = 0.42946 Z13 = 13.75000 X14 = −0.28026 Y14 = 0.41019 Z14 = 13.75000 X15 = −0.16708 Y15 = 0.37090 Z15 = 13.75000 X16 = −0.06101 Y16 = 0.31512 Z16 = 13.75000 X17 = 0.03739 Y17 = 0.24666 Z17 = 13.75000 X18 = 0.12836 Y18 = 0.16857 Z18 = 13.75000 X19 = 0.21234 Y19 = 0.08299 Z19 = 13.75000 X20 = 0.28987 Y20 = −0.00849 Z20 = 13.75000 X21 = 0.36169 Y21 = −0.10452 Z21 = 13.75000 X22 = 0.42876 Y22 = −0.20394 Z22 = 13.75000 X23 = 0.49185 Y23 = −0.30594 Z23 = 13.75000 X24 = 0.55150 Y24 = −0.40998 Z24 = 13.75000 X25 = 0.60805 Y25 = −0.51574 Z25 = 13.75000 X26 = 0.66170 Y26 = −0.62300 Z26 = 13.75000 X27 = 0.71262 Y27 = −0.73159 Z27 = 13.75000 X28 = 0.76096 Y28 = −0.84134 Z28 = 13.75000 X29 = 0.80669 Y29 = −0.95222 Z29 = 13.75000 X30 = 0.84982 Y30 = −1.06412 Z30 = 13.75000 X31 = 0.84982 Y31 = −1.06412 Z31 = 13.75000 X32 = 0.84981 Y32 = −1.07293 Z32 = 13.75000 X33 = 0.84381 Y33 = −1.07950 Z33 = 13.75000 X34 = 0.83505 Y34 = −1.08042 Z34 = 13.75000 X35 = 0.82795 Y35 = −1.07514 Z35 = 13.75000 X36 = −0.64316 Y36 = 0.15725 Z36 = 13.75000 X37 = −0.54266 Y37 = 0.13083 Z37 = 13.75000 X38 = −0.44308 Y38 = 0.10114 Z38 = 13.75000 X39 = −0.34575 Y39 = 0.06479 Z39 = 13.75000 X40 = −0.25111 Y40 = 0.02192 Z40 = 13.75000 X41 = −0.15926 Y41 = −0.02666 Z41 = 13.75000 X42 = −0.07058 Y42 = −0.08080 Z42 = 13.75000 X43 = 0.01478 Y43 = −0.14004 Z43 = 13.75000 X44 = 0.09706 Y44 = −0.20350 Z44 = 13.75000 X45 = 0.17646 Y45 = −0.27054 Z45 = 13.75000 X46 = 0.25307 Y46 = −0.34074 Z46 = 13.75000 X47 = 0.32697 Y47 = −0.41379 Z47 = 13.75000 X48 = 0.39816 Y48 = −0.48949 Z48 = 13.75000 X49 = 0.46663 Y49 = −0.56765 Z49 = 13.75000 X50 = 0.53243 Y50 = −0.64808 Z50 = 13.75000 X51 = 0.59564 Y51 = −0.73056 Z51 = 13.75000 X52 = 0.65641 Y52 = −0.81486 Z52 = 13.75000 X53 = 0.71503 Y53 = −0.90066 Z53 = 13.75000 X54 = 0.77197 Y54 = −0.98759 Z54 = 13.75000 X55 = 0.82795 Y55 = −1.07514 Z55 = 13.75000 X56 = −0.76951 Y56 = 0.20191 Z56 = 13.75000 X57 = −0.73964 Y57 = 0.18655 Z57 = 13.75000 X58 = −0.70796 Y58 = 0.17527 Z58 = 13.75000 X59 = −0.67564 Y59 = 0.16597 Z59 = 13.75000 X60 = −0.64316 Y60 = 0.15725 Z60 = 13.75000 F. Section height 14.25 X1 = −0.78638 Y1 = 0.24442 Z1 = 14.25000 X2 = −0.79786 Y2 = 0.21947 Z2 = 14.25000 X3 = −0.79834 Y3 = 0.19202 Z3 = 14.25000 X4 = −0.78777 Y4 = 0.16667 Z4 = 14.25000 X5 = −0.76792 Y5 = 0.14770 Z5 = 14.25000 X6 = −0.78638 Y6 = 0.24442 Z6 = 14.25000 X7 = −0.75683 Y7 = 0.27563 Z7 = 14.25000 X8 = −0.72171 Y8 = 0.30050 Z8 = 14.25000 X9 = −0.68360 Y9 = 0.32056 Z9 = 14.25000 X10 = −0.64379 Y10 = 0.33696 Z10 = 14.25000 X11 = −0.64379 Y11 = 0.33696 Z11 = 14.25000 X12 = −0.52804 Y12 = 0.36406 Z12 = 14.25000 X13 = −0.40913 Y13 = 0.36646 Z13 = 14.25000 X14 = −0.29181 Y14 = 0.34671 Z14 = 14.25000 X15 = −0.17925 Y15 = 0.30804 Z15 = 14.25000 X16 = −0.07333 Y16 = 0.25374 Z16 = 14.25000 X17 = 0.02552 Y17 = 0.18735 Z17 = 14.25000 X18 = 0.11744 Y18 = 0.11164 Z18 = 14.25000 X19 = 0.20242 Y19 = 0.02821 Z19 = 14.25000 X20 = 0.28088 Y20 = −0.06141 Z20 = 14.25000 X21 = 0.35357 Y21 = −0.15576 Z21 = 14.25000 X22 = 0.42137 Y22 = −0.25369 Z22 = 14.25000 X23 = 0.48506 Y23 = −0.35436 Z23 = 14.25000 X24 = 0.54525 Y24 = −0.45715 Z24 = 14.25000 X25 = 0.60240 Y25 = −0.56167 Z25 = 14.25000 X26 = 0.65677 Y26 = −0.66766 Z26 = 14.25000 X27 = 0.70863 Y27 = −0.77490 Z27 = 14.25000 X28 = 0.75809 Y28 = −0.88328 Z28 = 14.25000 X29 = 0.80513 Y29 = −0.99272 Z29 = 14.25000 X30 = 0.84986 Y30 = −1.10312 Z30 = 14.25000 X31 = 0.84986 Y31 = −1.10312 Z31 = 14.25000 X32 = 0.85006 Y32 = −1.11190 Z32 = 14.25000 X33 = 0.84425 Y33 = −1.11861 Z33 = 14.25000 X34 = 0.83554 Y34 = −1.11972 Z34 = 14.25000 X35 = 0.82837 Y35 = −1.11459 Z35 = 14.25000 X36 = −0.65970 Y36 = 0.10909 Z36 = 14.25000 X37 = −0.55900 Y37 = 0.08256 Z37 = 14.25000 X38 = −0.45944 Y38 = 0.05205 Z38 = 14.25000 X39 = −0.36209 Y39 = 0.01513 Z39 = 14.25000 X40 = −0.26745 Y40 = −0.02829 Z40 = 14.25000 X41 = −0.17559 Y41 = −0.07732 Z41 = 14.25000 X42 = −0.08652 Y42 = −0.13126 Z42 = 14.25000 X43 = −0.00027 Y43 = −0.18959 Z43 = 14.25000 X44 = 0.08317 Y44 = −0.25189 Z44 = 14.25000 X45 = 0.16377 Y45 = −0.31783 Z45 = 14.25000 X46 = 0.24152 Y46 = −0.38709 Z46 = 14.25000 X47 = 0.31658 Y47 = −0.45928 Z47 = 14.25000 X48 = 0.38899 Y48 = −0.53412 Z48 = 14.25000 X49 = 0.45873 Y49 = −0.61144 Z49 = 14.25000 X50 = 0.52580 Y50 = −0.69111 Z50 = 14.25000 X51 = 0.59024 Y51 = −0.77291 Z51 = 14.25000 X52 = 0.65226 Y52 = −0.85657 Z52 = 14.25000 X53 = 0.71222 Y53 = −0.94170 Z53 = 14.25000 X54 = 0.77070 Y54 = −1.02787 Z54 = 14.25000 X55 = 0.82837 Y55 = −1.11459 Z55 = 14.25000 X56 = −0.76792 Y56 = 0.14770 Z56 = 14.25000 X57 = −0.74232 Y57 = 0.13449 Z57 = 14.25000 X58 = −0.71526 Y58 = 0.12456 Z58 = 14.25000 X59 = −0.68757 Y59 = 0.11650 Z59 = 14.25000 X60 = −0.65970 Y60 = 0.10909 Z60 = 14.25000 G. Section height 14.75 X1 = −0.78588 Y1 = 0.19092 Z1 = 14.75000 X2 = −0.79741 Y2 = 0.16574 Z2 = 14.75000 X3 = −0.79777 Y3 = 0.13804 Z3 = 14.75000 X4 = −0.78690 Y4 = 0.11256 Z4 = 14.75000 X5 = −0.76667 Y5 = 0.09364 Z5 = 14.75000 X6 = −0.78588 Y6 = 0.19092 Z6 = 14.75000 X7 = −0.75225 Y7 = 0.22528 Z7 = 14.75000 X8 = −0.71190 Y8 = 0.25154 Z8 = 14.75000 X9 = −0.66807 Y9 = 0.27156 Z9 = 14.75000 X10 = −0.62218 Y10 = 0.28623 Z10 = 14.75000 X11 = −0.62218 Y11 = 0.28623 Z11 = 14.75000 X12 = −0.50725 Y12 = 0.30207 Z12 = 14.75000 X13 = −0.39136 Y13 = 0.29495 Z13 = 14.75000 X14 = −0.27818 Y14 = 0.26891 Z14 = 14.75000 X15 = −0.16978 Y15 = 0.22708 Z15 = 14.75000 X16 = −0.06735 Y16 = 0.17224 Z16 = 14.75000 X17 = 0.02915 Y17 = 0.10747 Z17 = 14.75000 X18 = 0.11964 Y18 = 0.03454 Z18 = 14.75000 X19 = 0.20347 Y19 = −0.04597 Z19 = 14.75000 X20 = 0.28103 Y20 = −0.13254 Z20 = 14.75000 X21 = 0.35309 Y21 = −0.22376 Z21 = 14.75000 X22 = 0.42024 Y22 = −0.31865 Z22 = 14.75000 X23 = 0.48320 Y23 = −0.41638 Z23 = 14.75000 X24 = 0.54268 Y24 = −0.51626 Z24 = 14.75000 X25 = 0.59929 Y25 = −0.61780 Z25 = 14.75000 X26 = 0.65348 Y26 = −0.72066 Z26 = 14.75000 X27 = 0.70562 Y27 = −0.82456 Z27 = 14.75000 X28 = 0.75569 Y28 = −0.92949 Z28 = 14.75000 X29 = 0.80381 Y29 = −1.03532 Z29 = 14.75000 X30 = 0.84987 Y30 = −1.14206 Z30 = 14.75000 X31 = 0.84987 Y31 = −1.14206 Z31 = 14.75000 X32 = 0.85034 Y32 = −1.15079 Z32 = 14.75000 X33 = 0.84477 Y33 = −1.15766 Z33 = 14.75000 X34 = 0.83613 Y34 = −1.15903 Z34 = 14.75000 X35 = 0.82888 Y35 = −1.15409 Z35 = 14.75000 X36 = −0.63239 Y36 = 0.05080 Z36 = 14.75000 X37 = −0.53411 Y37 = 0.02355 Z37 = 14.75000 X38 = −0.43776 Y38 = −0.00986 Z38 = 14.75000 X39 = −0.34375 Y39 = −0.04937 Z39 = 14.75000 X40 = −0.25239 Y40 = −0.09468 Z40 = 14.75000 X41 = −0.16372 Y41 = −0.14507 Z41 = 14.75000 X42 = −0.07730 Y42 = −0.19924 Z42 = 14.75000 X43 = 0.00701 Y43 = −0.25663 Z43 = 14.75000 X44 = 0.08899 Y44 = −0.31730 Z44 = 14.75000 X45 = 0.16831 Y45 = −0.38141 Z45 = 14.75000 X46 = 0.24478 Y46 = −0.44889 Z46 = 14.75000 X47 = 0.31879 Y47 = −0.51908 Z47 = 14.75000 X48 = 0.39043 Y48 = −0.59167 Z48 = 14.75000 X49 = 0.45960 Y49 = −0.66662 Z49 = 14.75000 X50 = 0.52618 Y50 = −0.74388 Z50 = 14.75000 X51 = 0.59026 Y51 = −0.82324 Z51 = 14.75000 X52 = 0.65202 Y52 = −0.90440 Z52 = 14.75000 X53 = 0.71194 Y53 = −0.98694 Z53 = 14.75000 X54 = 0.77066 Y54 = −1.07034 Z54 = 14.75000 X55 = 0.82888 Y55 = −1.15409 Z55 = 14.75000 X56 = −0.76667 Y56 = 0.09364 Z56 = 14.75000 X57 = −0.73476 Y57 = 0.07849 Z57 = 14.75000 X58 = −0.70100 Y58 = 0.06799 Z58 = 14.75000 X59 = −0.66672 Y59 = 0.05929 Z59 = 14.75000 X60 = −0.63239 Y60 = 0.05080 Z60 = 14.75000

While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment(s), but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims, which scope is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures as permitted under the law. Furthermore it should be understood that while the use of the word preferable, preferably, or preferred in the description above indicates that feature so described may be more desirable, it nonetheless may not be necessary and any embodiment lacking the same may be contemplated as within the scope of the invention, that scope being defined by the claims that follow. In reading the claims it is intended that when words such as “a,” “an,” “at least one” and “at least a portion” are used, there is no intention to limit the claim to only one item unless specifically stated to the contrary in the claim. Further, when the language “at least a portion” and/or “a portion” is used the item may include a portion and/or the entire item unless specifically stated to the contrary. 

1. An airfoil comprising: an external surface having first and second sides, the external surface extending spanwise between a hub and a tip and streamwise between a leading edge and a trailing edge; and the external surface having a contour substantially defined by Table 1 as listed in the specification.
 2. The airfoil of claim 1, further comprising: at least one coating formed on the external surface thereof.
 3. The airfoil of claim 2, wherein the external surface including the at least one coating substantially meets the contour dimensions defined by Table
 1. 4. The airfoil of claim 2, wherein an outer surface of the at least one coating extends outside of the contour dimensions as substantially defined by Table
 1. 5. The airfoil of claim 2, wherein the coating includes at least one of a thermal barrier coating and a radiation barrier coating.
 6. The airfoil of claim 1, wherein a portion of the external surface includes at least one discontinuity.
 7. The airfoil of claim 6, wherein the at least one discontinuity includes a through aperture formed in at least one of the sides of the airfoil to provide an outlet path for cooling fluid to flow therethrough.
 8. The airfoil of claim 1, wherein the airfoil is connected to a first stage turbine nozzle guide vane assembly.
 9. The airfoil of claim 1, wherein the positional tolerance of the external surface is held to range of about ±0.025 inches for each dimension listed in Table
 1. 10. A turbine nozzle guide vane assembly for a gas turbine engine comprising: an inner shroud having an upper surface and a lower surface, the upper surface of the inner shroud partially defining an inner flow path wall; an airfoil extending radially outward from the upper surface of the inner shroud relative to an axis of rotation of the gas turbine engine, the airfoil having first and second three-dimensional external surfaces extending between a hub and a tip in a spanwise direction and between a leading edge and a trailing edge in a streamwise direction; and a Cartesian coordinate array having X,Y and Z axis coordinates listed in Table 1 of the specification defining the first and second external surfaces of the airfoil, wherein the Z axis generally extends radially outward from at least one of the upper surface of the inner shroud or a longitudinal axis of the engine, the X axis generally extends normal to the Z axis in the streamwise direction, and the Y axis generally extends normal to both the X axis and the Z axis in a lateral direction.
 11. The turbine nozzle guide vane assembly of claim 10, wherein the external surface of the airfoil is formed within a manufacturing tolerance of about ±0.025 inches of each dimension listed in Table
 1. 12. The turbine nozzle guide vane assembly of claim 10, wherein the Z axis further defines a stacking axis extending at a predefined angle from the inner shroud.
 13. The turbine nozzle guide vane assembly of claim 12, wherein the angle of the stacking axis is located between a normal position and 25° from the normal position in any direction.
 14. The turbine nozzle guide vane assembly of claim 10, further comprising: at least one coating formed on the external surface of the airfoil.
 15. The turbine nozzle guide vane assembly of claim 14, wherein the at least one coating is applied to the airfoil such that an outer surface of the coating is located within a tolerance of ±0.050 inches of the coordinate dimensions defined in Table
 1. 16. The turbine nozzle guide vane assembly of claim 14, wherein the coating is at least one of a thermal barrier coating and a radiation barrier coating.
 17. The turbine nozzle guide vane assembly of claim 10, wherein a portion of the external surface of the airfoil includes at least one discontinuity.
 18. The turbine nozzle guide vane assembly of claim 17, wherein the at least one discontinuity includes a through aperture formed in at least one of the sides of the airfoil to provide an outlet path for cooling fluid to flow therethrough.
 19. The turbine nozzle guide vane assembly of claim 10, wherein the airfoil includes an outer shroud formed adjacent the tip.
 20. A method of forming an airfoil for a turbine nozzle guide vane comprising: forming a contoured three-dimensional external surface of an airfoil defined by Cartesian (X, Y and Z) coordinates listed in the specification as Table 1, wherein the Z axis coordinates are generally measured from an inner shroud or an engine centerline axis, the X axis coordinates are generally measured normal to the Z axis in a streamwise direction, and the Y axis coordinates are generally measured normal to the Z axis and normal to the X axis.
 21. The method of claim 20, further comprising: forming the airfoil from a casting process, wherein the casting process includes one of integrally casting the turbine nozzle guide vane in one piece and casting multiple pieces and subsequently bonding the cast pieces together.
 22. The method of claim 20, further comprising: forming the airfoil from a wrought material; and machine processing a portion of the airfoil to meet a design specification. 